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Doeblin and Modern Probability
Edited by: Harry Cohn
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Contemporary Mathematics
1993; 347 pp; softcover
Volume: 149
ISBN-10: 0-8218-5149-7
ISBN-13: 978-0-8218-5149-4
List Price: US$60
Member Price: US$48
Order Code: CONM/149
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Wolfgang Doeblin, one of the greatest probabilists of this century, died in action during World War II at the age of twenty-five. He left behind several seminal contributions which have profoundly influenced the field and continue to provide inspiration for current research. This book is based on papers presented at the conference, "Fifty Years after Doeblin: Developments in the Theory of Markov Chains, Markov Processes, and Sums of Random Variables," held at Blaubeuren, Germany, in November 1991. Presented here for the first time is an account of Doeblin's life and work, revealing the circumstances of his tragic death in 1940. Organized into sections according to topic, the papers describe both Doeblin's original contributions as well as current developments. With contributions by top probabilists from sixteen countries, this book will interest both researchers in probability and science historians.

Readership

Researchers in probability and science historians.

Table of Contents

  • Doeblin's Life and Work
  • B. Bru -- Doeblin's life and work from his correspondence
  • K. L. Chung -- Reminiscences of one of Doeblin's papers
  • Coupling
  • T. M. Liggett -- The coupling technique in interacting particle systems
  • H. Thorisson -- Coupling and shift-coupling random sequences
  • Continued Fractions and Ergodicity
  • M. Iosifescu -- Doeblin and the metric theory of continued fractions: A functional theoretic solution to Gauss' 1812 problem
  • M. Iosifescu -- A basic tool in mathematical chaos theory: Doeblin and Fortet's ergodic theorem and Ionescu Tulcea and Marinescu's generalization
  • M. Iosifescu and S. Kalpazidou -- The nearest integer continued fraction expansion: An approach in the spirit of Doeblin
  • Independent and Weakly Dependent Random Variables
  • M. Csörgő, L. Horváth, Q.-M. Shao, and B. Szyszkowicz -- On the weighted asymptotics of partial sums and empirical processes of independent random variables
  • M. Gordin -- Homoclinic approach to the central limit theorem for dynamical systems
  • M. Peligrad -- Asymptotic results for \(\varphi\)-mixing sequences
  • M. Rosenblatt -- The central limit theorem and Markov sequences
  • Homogeneous and Non-homogeneous Markov Chains
  • I. Fleischer and A. Joffe -- Behaviour of infinite products with applications to non-homogeneous Markov chains
  • E. Seneta -- Applications of ergodicity coefficients to homogeneous Markov chains
  • Markov Processes
  • I. Cuculescu -- Applications of some constructions of Markov processes
  • S. P. Meyn and R. L. Tweedie -- The Doeblin decomposition
  • S. P. Meyn and R. L. Tweedie -- Generalized resolvents and Harris recurrence of Markov processes
  • Stochastic and Nonstochastic Matrices
  • J. E. Cohen, Y. Derriennic, and Gh. Zbaganu -- Majorization, monotonicity of relative entropy, and stochastic matrices
  • H. Cohn -- Products of stochastic, nonstochastic, and random matrices
  • J. Hajnal -- Shuffling with two matrices
  • Stochastic Processes
  • K. B. Athreya -- Continuous time gambling problems
  • E. Bolthausen -- Stochastic processes with long range interactions of the paths
  • A. Mukherjea -- Some remarks on products of random affine maps on \((R^+)^d\)
  • P. E. Nüesch -- A multivariate look at E. Sparre Andersen's equivalence principle
  • P. Ney and E. Nummelin -- Regeneration for chains of infinite order and random maps
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